Method and apparatus for reproducing blended colorants on an electronic display

ABSTRACT

An apparatus and method for reproducing the color of blended colorants on an electronic display such as a cathode ray tube, liquid crystal display or other type of electronic device that utilizes RGB values. Predictions of blended colorants on or in substrates can be made from XYZ measurements of samples prepared with no colorants, one colorant, and pairs of colorants. The calculation method uses light absorption, light scattering, and light absorption blend coefficients. An image digitizer can be used to obtain XYZ values from samples. Furthermore, image digitizer RGB values are converted into XYZ values with a non-linear model using a simple method. Furthermore, the above process to generate XYZ values from image digitizer RGB values can be used to generate RGB values from XYZ values for electronic display.

This application is a continuation of prior application Ser. No.07/859,339, filed on Mar. 27, 1992 now abandoned.

BACKGROUND OF THE INVENTION

This invention relates to a method and apparatus for reproducing thecolor of blended colorants on an electronic display.

The most accurate ways of computing color formulation are either verydifficult to use, or computationally impractical. The most successfulsimple mathematical theory for predicting the color of mixtures is theKubelka-Munk Model. For some applications, the model is overlysimplistic. The Kubelka-Munk Model assumes light falls exactlyperpendicular onto a perfectly flat media containing the colorants. Thecolorants must be perfectly mixed into the substrate media, and theresulting colored substrate must be isotropic. The index of refractionof the media and colorants is assumed to be the same as air, so internaland external specular reflection and refraction are ignored.

Assume these conditions are met, and the substrate is optically thick.In this case, Kubelka-Munk Theory predicts the following simplerelationship: K/S=(1-R)² /2R. K and S are physical properties of thecolored media. R is the measured color. The relationship expressed bythe equation holds at each wavelength of light in the visible spectralband. R denotes the fraction of light reflected by the sample. K and Sare light absorption and light scattering coefficients of the colorantmixture, respectively. It is more convenient to deal with K/S ratherthan R. This is because the physical properties of a mixture (K and S)are, to a good approximation, proportional to the physical properties ofeach colorant in the mixture, namely the corresponding coefficientsK_(i) and S_(i) of colorant i. The proportionality constants arecomponent concentrations C_(i). Therefore, for simple colorantformulation calculations, one assumes for N colorants that K=K₁ C₁ +K₂C₂ +. . . K_(N) C_(N) and S=S₁ C₁ +S₂ C₂ +. . . S_(N) C_(N). As before,these equations hold at each wavelength of light. By inverting theearlier formula (K/S=(1-R)² /2R) that connects K/S to R, and by usingthe above equations connecting K and S to K_(i) and S_(i), a connectionis obtained between colorant concentrations C_(i) and measured color R.Values of absorption and scattering coefficients of colorants aretypically extracted from least squares calculations involving samplecolor measurements.

For applications requiring a high degree of accuracy, this simpleKubelka-Munk Theory must be modified. Corrections for substrate surfacereflection, internal refraction, and colorant interactions arenecessary. Sometimes it is necessary to extend spectral measurementsinto the ultraviolet to deal with colorant fluorescence. The texture ofsome targets (e.g., textiles) have a gloss that cannot be easilysubtracted by measurement or compensated for by mathematical modeling.This means computed values for K_(i) and S_(i) must be cautiouslyinterpreted, and perhaps further modified, before subsequent colorantformulation predictions are accurate.

In computer aided design (CAD), visual feedback is desirable duringcolor formulation. One way to do this is to simulate a product on anelectronic display. Performing Kubelka-Munk calculations, with thecorrections noted above, involves a great deal of computation. Spectraldata at many wavelengths must be stored on computer. Color measurementsare traditionally made with spectrophotometers. These devices arerelatively expensive and require uncommon technical expertise tooperate. The usual way of converting spectral data into colorcoordinates appropriate for electronic display involves complexnonlinear equations. Computer aided design is one example of anapplication where color precision requirements are less demanding than,say, textile dye formulation. The present invention solves theseproblems, in a manner not disclosed in the known prior art, for lessdemanding applications.

SUMMARY OF THE INVENTION

This Application discloses an apparatus and method for reproducingblended coloration of samples on an electronic display. The electronicdisplay can be a cathode ray tube, liquid crystal display, or other typeof electronic display utilizing red, green, and blue (RGB) colorcoordinates. We usually assume colorants are blended and not merelyplaced on the substrate in side-by-side relation. Colorants can beapplied in layers, if the colorants are mostly transparent, not veryopaque. Color image digitizers are commonly used during some kinds ofcomputer aided design. We show how color image digitizers, lessexpensive than traditional color measurement equipment, can be used toobtain color measurements. This invention is for simulation work onlyand cannot be used for critical colorant formulation work.

We choose CIE XYZ tristimulus color coordinates for color analysis.Instead of measurements over many different wavelengths, tristimuluscolor measurements X, Y, and Z, are averages over red, green, and bluespectral bands, respectively. This is the minimum spectral informationrequired to quantify color, since color vision provides the brain withred, green and blue spectral band averages via retina cone cells. And,this is why electronic displays use three-color light emission systems;e.g., CRT color monitors use red, green, and blue phosphors. Devicesthat measure color at many wavelengths (such as spectrophotometers andradiometers) compute XYZ values from appropriate weighted averages inthe red, green, and blue spectral bands. Devices such as colorimeters,color luminance meters, and desktop image digitizers are less expensivebecause XYZ values are directly measured using three color opticalfilters. Each filter performs the appropriate spectral band averagesdirectly. That is, color is measured essentially at only three or fourwavelengths for these latter devices.

Whenever possible, a color image digitizer is preferable to acolorimeter because it is less expensive and requires less technicalexpertise to operate. Color image digitizer operation can be more easilyincorporated into an application than devices like spectrophotometers. Acolor image digitizer is also more likely to be considered necessary forother activities, such as image acquisition.

Color image digitizers are less accurate than full spectrum measurementdevices, but we are only considering applications where high accuracy isunnecessary. For example, visual feedback for CRT color monitor imageryrequires less accuracy than, say, product color quality control in amanufacturing operation. Human color vision is very accommodating tosystematic deviations from color accuracy.

The use of XYZ values violates Kubelka-Munk Model assumptions becausethe derivation treats radiation scattering at each wavelength. Weightedaverages of wavelengths have no physical meaning in the model. Using XYZvalues in the Kubelka-Munk Model leads to incorrect predictions forcolorant mixtures. It is necessary to add additional terms to the modelto achieve satisfactory predictions. The previously stated equations forK and S contain terms of the form K_(i) C_(i) and S_(i) C_(i). Wediscovered that it is sufficient to add terms of the form K_(ij) C_(i)C_(j) to the equation for K. We refer to the coefficients K_(ij) aslight absorption blend coefficients for colorants i and j. It is notnecessary to add similar terms to S. These new coefficients aregenerally not related to molecular interactions between colorants in themixing media, although the addition of these terms might betteraccommodate such interactions when present. In this invention, leastsquares fitting to our modified Kubelka-Munk equations partiallycompensates for factors such as specular reflection, non-smooth surfaces(e.g., textiles), the use of tristimulus color measurements, and otherfactors not included in simple Kubelka-Munk Theory.

If colorants are applied in thin layers on a substrate, rather than wellmixed into a substrate, our technique can also successfully predictcolors. If colorants are mostly transparent, and not very opaque, thenone can use the term K_(ij) C_(i) C_(j) in calculations when colorant jis applied to colorant i, and use the term K_(ji) C_(i) C_(j) whencolorant i is applied to colorant j. K_(ij) and K_(ji) will differ invalue to a degree that correlates with colorant opacity. Clearly, alight colorant applied to a dark colorant will appear lighter than adark colorant applied to a light colorant, in general. For the remainderof this Application, we assume this distinction is not necessary tosimplify the Application. When colorants well mixed, then K_(ij) equalsK_(ji), whether or not colorants are opaque.

The first step necessary to compute absorption and scatteringcoefficients is to gather sample measurements. We measure X, Y, Ztristimulus color measurements from an uncolored substrate. (All of thesamples discussed below must be prepared using the same type ofsubstrate. In applications where substrates are different, eachsubstrate must be treated as a separate case). Then X, Y, Z tristimuluscolor measurements are made from samples with different concentrationsof one colorant. This is done for all colorants to be blended, andconcentrations must span the practical limit of concentrations. Finally,X, Y, Z tristimulus color measurements are made from samples utilizingpairs of colorants at several concentrations so that the sum of theblend concentrations is some fixed limit, stated in relative terms as100%. All concentrations in this Application are expressed as apercentage. This relative scale must be based on some absolute physicalmeasurement, such as colorant weight or volume.

The total concentration limit is usually due to some physical constrainton the colorant application process. For example, the amount of acolorant that can diffuse into a textile polymer has an upper limit.Small extrapolations beyond 100% are predicted satisfactorily ininstances where the practical limit chosen for manufacturing purposes isless than the actual physical limit.

Now we begin to utilize the measurements obtained in the first step. Thesecond step is to compute the light absorption coefficient K_(o) for theuncolored substrate using measurements from the uncolored substrate. Thethird step is to utilize the measurements from the substrate colored bya single colorant to compute the light absorption coefficients K_(i) andlight scattering coefficients S_(i) for colorant i. The final steputilizes the two-colorant blend measurements to compute the lightabsorption blend coefficient K_(ij) for each pair of colorants i and j.All of these coefficients are computed for the X, Y, and Z (red, green,and blue) spectral bands. We have discovered that it is not necessary toextend the model to higher order terms. There is no S_(o) term for thecolorant substrate, because in our procedure this substrate lightscattering term is factored into the other coefficients.

K_(o), K_(i), S_(i), and K_(ij) represent coded summaries of all thesample measurements. Less computer resources are necessary to storethese coefficients than is necessary to store the measurements used toobtain the coefficients. These stored coefficients comprise a compactdatabase for color prediction. Least squares fitting eliminates samplemeasurement variability from future calculations. This means using thecoefficients to compute a color gradient always produces a visuallyuniform color series. These are important advantages over interpolationschemes based on many color measurements, when such a method isunwarranted.

Once the coefficients are used to compute K/S values for arbitraryblends, which in turn is converted into color as XYZ values, these XYZvalues can be used to compute RGB color coordinates used to show theblends on an electronic display.

It is an advantage of this invention to predict the color of a blend ofcolorants on substrates without having to actually manufacture a samplewith this blend of colorants.

Still another advantage of this invention is that an image digitizer canbe used to convert data into standard XYZ color measurements.

Another advantage of this invention is that predicting the blend of morethan two colorants does not require the manufacturing of samples withmore than two colorants.

A further advantage of this invention is that specular reflection,nonsmooth surfaces (e.g., textiles), layers of mostly transparentcolorants (e.g., computer hardcopy colorants), and tristimulus colormeasurements can be accommodated, even though these conditions are notappropriate in the traditional Kubelka-Munk model.

Yet another advantage is a unique method of converting X, Y, Z valuesinto R, G, B values and visa versa without having to linearize theirnonlinear relationship. This advantage applies to RGB values for CRTcolor display, and RGB values obtained from an image digitizer.

These and other advantages will be in part apparent and in part pointedout below.

BRIEF DESCRIPTION OF THE DRAWINGS

The above as well as other objects of the invention will become moreapparent from the following detailed description of the preferredembodiments of the invention when taken together with the accompanyingdrawings, in which:

FIG. 1 is a schematic block diagram of the basic elements forreproducing blended coloration of a substrate on an electronic display;

FIG. 2 is a flowchart of the steps utilized in measuring color of asample by means of an image digitizer;

FIG. 3 is a graph of Macbeth® Colorchecker® Color Rendition Chart colorchromaticities comprised of six shades of gray, three additive primaries(red, green, blue), three subtractive primaries (yellow, magenta, cyan),two skin colors, and ten miscellaneous colors which collectively spanmost of color space, and the graph shows the gamut of chromaticitiesavailable on a CRT color monitor;

FIG. 4 is a graph of image digitizer RGB values with measured andpredicted XYZ values, and image digitizer model parameters, for Macbeth®gray shades;

FIG. 5 is a graph of measurements versus predictions for all Macbeth®colors;

FIG. 6 is a flowchart of the steps utilized to predict colorant blendson a substrate;

FIG. 7 is a chart showing the series of four calculations necessary tocompute K_(o), K_(i), S_(i), and K_(ij) coefficients for colorants thatare dyes;

FIG. 8 is a flowchart of the steps utilized in displaying colormeasurements on a cathode ray tube or other RGB electronic imagedisplay;

FIG. 9 is a graph of cathode ray tube (CRT) RGB values with measured andpredicted XYZ values, and CRT model parameters; and

FIG. 10 is a graph of cathode ray tube measurements versus predictionsfor all measured phosphor colors.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Refer now to the accompanying flowcharts and graphs. FIG. 1 shows aschematic diagram of the basic elements for reproducing blendedcoloration on an electronic display using computer technology. Boxes inthe diagram either represent computer information modules (algorithms,databases) or external measurement devices (colorimeters,spectrophotometers). Labeled arrows represent the flow of specifiedinformation between computer modules or external measurement devices.

One color measurement standard for computer aided design ormanufacturing systems is the CIE XYZ tristimulus color coordinates. Itis used for both color input (image digitizers, on-line colorimeters,colorant formulation databases), and color output (color monitors, colorprinters, colorant formulation databases). This standardized colorcoordinate system has been an international standard for seventy years.The use of XYZ values is increasingly being used as the basis forcomputerized processes involving color. Even companies with proprietarycolor coordinate systems that offer advantages for specific applicationscan usually convert their color coordinates into XYZ color coordinates.One reason for preferring XYZ values over other standard colorcoordinates is that they directly correspond to RGB color systems usedby devices such as image digitizers and electronic displays.

XYZ values measured with a colorimeter are dimensionless, and areusually expressed as a percentage. The percent sign is customarilyomitted. XYZ measurements are made with respect to some illuminantstandard, such as D65 (day light at a black body temperature of 65,000°K.). These relative color values are used to quantify the color ofobjects that do not emit light. Percentages indicate the fraction ofwhite light that is reflected from a target in the red, green, and bluespectral bands. Some objects emit light, such as the phosphors of a CRTcolor monitor. Then absolute XYZ values are measured in dimensions suchas candelas per square meter or foot-Lamberts. Absolute XYZ values canbe converted into relative XYZ values by scaling them with respect tosome standard emitter of white light.

It is common for measurements to be expressed in terms of chromaticity xand y, and "luminance" Y. Conversion between XYZ values to xyY values isgiven by x=X/(X+Y+Z), and y=Y/(X+Y+Z). Y is the same in both coordinatesystems. Chromaticity coordinates x and y are dimensionless and expressthe relative proportion of red and green in a color. The relative amountof blue is z=1-x-y. A color with equal amounts of red and green havex=y=z=1/3. Y is sometimes chosen as a measure of luminance (intensity,brightness) because human vision is more sensitive to green than red orblue. Chromaticities of common colors are shown in FIG. 3. Also shown isthe chromaticity range of a typical CRT color monitor used for computeraided design.

Although color measurements are traditionally obtained from colorimeters2 or spectrophotometers 3, or chroma meters (not shown) the preferredmethod in this Invention involves the use of an image digitizer 1, asshown in FIG. 1. Image digitizers like those manufactured by SharpElectronics Corporation located at Mahwah, N.J., also have red, green,and blue receptors, or flash red, green, and blue light on samples.However, current image digitizers typically do not return XYZ values, orany other standard color coordinate system. Such devices commonly returna set of RGB values, indicating the strength of red, green, and blue.Red, green, and blue image digitizer color components are denoted as R,G, and B respectively. RGB values commonly range from 0 through 255.This Application discloses how to convert from scanner RGB values torelative XYZ values.

The image digitizer, 1 in FIG. 1, scans a sample and provides imagedigitizer RGB values for each measurement area in the sample.Computations upon this RGB data is performed by the Image DigitizerModel Algorithm 5. Before RGB values can be converted into XYZ values in5, certain prerequisite measurements and calculations must be performed.In phase one of the prerequisite work, color target shades of grayhaving identical chromaticity xy are scanned by the image digitizer.These measurements are used to compute model parameters that arecharacteristic of the red, green, and blue image digitizer lightmeasurement channels. In phase two, all of the target colors are used tocompute a mixing matrix. The mixing matrix is used to convert all imagedigitizer RGB values into XYZ values.

A color target must be chosen for the image digitizer, to be used asdescribed in the previous paragraph. The target must have several shadesof gray with identical chromaticities. It must also have several colorsthat span the major color chromaticities. Very elaborate color targetsare under development for color critical industries. One such colortarget standard is offered by the American National Standards Institute(ANSI) IT8 committee for graphic arts. Both transparent (ANSI IT8.7-1)and reflectance (ANSI IT8.7-2) targets will be offered by the majorphotographic film manufacturers by mid-1992. For our purposes, it issufficient to use Macbeth® ColorChecker® Color Rendition Chart.

The Macbeth® ColorChecker® Color Rendition Chart has been a reliablecolor standard for photographic and video work for the last 15 years.The Macbeth® chart has 24 colors, as shown in TABLE 1, with chromaticitycoordinates based on CIE illuminant C. Colors include six shades ofgray, three additive primaries (red, green, blue), three subtractiveprimaries (yellow, magenta, cyan), two skin colors, and tenmiscellaneous colors. Chromaticities of chart colors span most of colorspace, as shown in FIG. 3. FIG. 3 also shows the gamut of chromaticitiesavailable on a typical CRT color monitor.

CIE color measurements are provided by Macbeth® for each color in theMacbeth® chart, and reproduced in TABLE 1. Alternatively, a colorimeterof choice can be used to measure the Macbeth® colors. While using themeasurements supplied by Macbeth® for calculations is convenient, thisis not the preferred method. A standard colorimeter should be chosen forall measurements made for a computer aided design process. For example,if a HunterLab® LabScan, manufactured by Hunter Lab of Reston, Va., isused to measure all product samples, then it is preferable to measurethe Macbeth® chart colors with the HunterLab® LabScan. Then thecorrespondence between future sample measurements and image digitizermeasurements would be as close as possible. This is because differentmodels of colorimeters, even when manufactured by the same company,often give different CIE color measurements. For example, colorimeterstreat specular reflection differently. Colorimeters use different sampleillumination geometries. This step of collecting RGB and XYZ values oftarget colors is designated as numeral 20 in FIG. 2. In this document,RGB and XYZ values are normalized so values fall between 0 and 1. Thisstep is denoted in FIG. 2 by numeral 30.

Tristimulus values for red, green, and blue image digitizer channels aredenoted X_(r), Y_(g), and Z_(b), respectively, and we refer to themgenerically as X_(r) Y_(g) Z_(b) values. They are defined only for grayshades having the same neutral chromaticity. They are computed from thegray shade light measurements, and are used in subsequent calculationsto characterize the performance of the image digitizer light sensors.Gray shades can be provided by the Macbeth® ColorChecker®. These shadesof gray all have chromaticity x=0.310 and y=0.316, and are colors 19through 24 shown in TABLE 1.

Image digitizer parameters characterizing the non-linearity betweenimage digitizer RGB values and XYZ values are denoted as g_(r), g_(g),and g_(b), respectively. These are generically referred to as "gamma" org.

Image digitizer parameters characterizing red, green and blue channelcontrast are denoted as G_(r), G_(g), and G_(b), respectively. These aregenerically referred to as "gain" or G.

Image digitizer parameters characterizing red, green and blue channelbrightness are denoted as O_(r), O_(g), and O_(b), respectively. Theseare generically referred to as "offset" or O.

Our choice of notation, and the terms "gamma", "gain", and "offset"derive from their original use for mathematically modeling cathode raytube display devices.

Gain, offset and gamma parameters in the image digitizer model establisha quantitative relationship between measured color (XYZ tristimulusvalues) and image digitizer color components (RGB values) for the red,green, and blue image digitizer channels, as shown in the followingequations

    X.sub.r =(G.sub.r +O.sub.r *R).sup.gr                      Eq. 1.0

    Y.sub.g =(G.sub.g +O.sub.g *G).sup.gg                      Eq. 1.1

    Z.sub.b =(G.sub.b +O.sub.b *B).sup.gb                      Eq. 1.2

We now explain how to compute the image digitizer model parameters fromthe Macbeth® ColorChecker® color measurements. XYZ measurements valuesare selected for shades of gray having the same chromaticity, xy. Colors19 through 24 (TABLE 1) are shades of gray with identicalchromaticities. These are identified as the X_(r) Y_(g) Z_(b) values.Each gray shade has corresponding image digitizer RGB values. This stepis designated as numeral 40 in FIG. 2. The next step is designated asnumeral 50 in FIG. 2, which is to chose whether to treat the X, Y, or Zdata. Usually, one proceeds in the order X component, then Y component,and then Z component. The order is unimportant. TABLE 2 shows an exampleof image digitizer RGB values for Macbeth® colors. Equations 1.0, 1.1and 1.2 are in the following form (x and y are not chromaticityvariables here):

    y=(G+O*x).sup.g                                            Eq. 2.0

Equation 2.0 can be rewritten as an equation that is linear in y^(1/g).That is, a graph of x as a function of y^(1/g) is a straight line.

    y.sup.1/g =G+o*x                                           Eq. 2.1

For specific values of g, G, and O, we define a least squares error E. Asubscript m denotes individual gray shade measurements x_(m)(representing R_(m) or G_(m) or B_(m)) and y_(m) ^(1/g) (representingX_(rm) ^(1/gr) or Y_(gm) ^(1/gg) or Z_(bm) ^(1/gb)). There is a total ofN gray shade measurements, so m ranges from 1 to N. ##EQU1##

For computational purposes, an expanded form of Equation 2.2 ispreferred. Equation 2.3 is expressed in terms of summations that willalready exist in prior computational steps in the final algorithm.

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S                                                Eq. 2.3

The following summation equations determine the "S" variable values.##EQU2## Note the variable S found in Equation 2.4, is equal to thenumber of shades of gray.

Equation 2.1 is nonlinear in g. Because of this nonlinearity, ourapproach is not to minimize the least squares error found in Equation2.3 for g, G, and O simultaneously. Instead, we pick a reasonable valuefor g, and find G and O that minimize the least squares error. The stepof choosing g is designated by numeral 60 in FIG. 2. For this g, G and Oare computed from by Equations 3.0, 3.1 and 3.2. This is designated bynumeral 70 in FIG. 2. These equations are solutions to the least squaresfit for a given value of g.

    D=S.sub.xx S-S.sub.x.sup.2                                 Eq. 3.0

    G=(S.sub.xx S.sub.y -S.sub.x S.sub.xy)/D                   Eq. 3.1

    O=(-S.sub.x S.sub.y +S S.sub.xy)/D                         Eq. 3.2

Our chosen g and the computed optimal values for G and O can be put intoEquation 2.3 to compute the least squares error E (or E²) as designatedby numeral 80 in FIG. 2. We then can pick another value of g, whichallows us to compute another set of optimal values of G and O, that inturn gives a new least squares error. This decision to select another gis designated by numeral 90 in FIG. 2. For two choices of g, the bettervalue is the one giving the smaller least squares error E (or E²). Theleast squares error is not very sensitive to changes in g by differencesof 0.25. The algorithm chooses values of g from 1 through 5 inincrements of 0.25 As outlined above, for each g, compute G and O fromEquations 2.4 through 2.9, and 3.0 through 3.2, and least squares errorE² from Equation 2.3 The best value of g is the one minimizing E². Thisfinal selection of g is designated by numeral 100 in FIG. 2.

As previously stated with regard to numeral 50 of the flowchart in FIG.2, this calculation is repeated separately for the red, green, and bluecomponents of the gray shades. This decision step is designated bynumeral 110 in FIG. 2, which will lead to repeating steps 60, 70, 80, 90and 100 in FIG. 2 for each spectral band.

Once gamma, gain, and offset parameters are computed, Equations 1.0,1.1, and 1.2 predict X_(r), Y_(g), and Z_(b) for gray shades withchromaticities matching the original gray shades. For the Macbeth®chart, Equations 1.0, 1.1 and 1.2 then accurately predict all shades ofgray with a chromaticity equal to x=0.310, y=0.316. Equations 1.0, 1.1and 1.2 do not by themselves accurately predict arbitrary colors.

The next step is to use measurements of arbitrary colors so we canconvert image digitizer RGB values of arbitrary colors into XYZ values(or vice versa). One of Grassman's Laws provides an approximate way tocalculate tristimulus values for arbitrary colors. It is applicablebecause image digitizer channels are largely independent (i.e., thechannels measure primary colors). Therefore, additive color mixing isappropriate. A mixing matrix M produces a linear combination of the grayshade tristimulus values. Define the column matrix of measured XYZvalues for any color as: ##EQU3## and the column matrix of predicted XYZvalues computed from Equations 1.0, 1.1 and 1.2, as: ##EQU4## Then X andX_(rgb) are connected by the linear relationship

    X=MX.sub.rgb                                               Eq. 4.2

where M is a 3×3 matrix. M is computed from all target colors, includingshades of gray, in a least squares (pseudo-inverse) fashion, as follows.Define a 3×N matrix Q whose columns are N color target measurementsX_(m) of the type shown in Equation 4.0 as follows:

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |Eq. 4.1

Also define a 3×N matrix Q_(rgb) containing the corresponding imagedigitizer channel tristimulus predictions obtained from Equations 1.0,1.1 and 1.2 for the same N measurements as follows:

    Q.sub.rgb =|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN |                                                Eq. 4.4

The computation of Q and Q_(rgb) from XYZ measurements and estimates ofall target colors is designated as numeral 120 in FIG. 2. The columns ofQ and Q_(rgb) are connected by matrix M from Equation 4.2, so therefore:

    Q=MQ.sub.rgb                                               Eq. 4.5

This holds true if the image digitizer model (Equations 1.0, 1.1 and1.2) is exactly true and color measurements are without error. The modeland data are not exact, so the "best" (least squares) solution isobtained by solving Equation 4.5 using a pseudo-inverse as follows:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1                      Eq. 4.6

Superscript T denotes matrix transpose, and superscript -1 denotesmatrix inverse. The computation of M is designated by numeral 130 inFIG. 2. The inverse is computed for a 3×3 matrix. Once the gain, offset,gamma, and mixing matrix M are known, Equations 1.0, 1.1, 1.2 and 4.2are used to convert image digitizer R, G, and B into X, Y, and Z for anycolor. This step is designated by numeral 140 in FIG. 2. This conversionconstitutes the image digitizer model algorithm denoted by numeral 5 inFIG. 1. In an application, such a conversion might be used to obtain XYZvalues for the color database denoted by numeral 7 in FIG. 1.

The inverse transformation, converting X, Y, and Z into R, G, and B, iscomputed as follows:

    X.sub.rgb =M.sup.-1 X                                      Eq. 5.0

    R=(X.sub.r.sup.1/gr -G.sub.r)/O.sub.r                      Eq. 5.1

    G=(Y.sub.g.sup.1/gg -G.sub.g)/O.sub.g                      Eq. 5.2

B=(Z_(b) ^(1/gb) -G_(b))/O_(b) Eq. 5.3

Once gamma, gain, and offset are computed for a device, they can besaved in a computer data structure for all future color conversions.That is, only the step labeled 140 in FIG. 2 is necessary for subsequentcolor conversions. These image digitizer parameters are independent ofthe types of target measured by the image digitizer. XYZ values fortextiles, paper products, photographs, and so on, can be computed fromRGB values using the same parameter values.

TABLE 2 shows an example of image digitizer RGB values, and TABLE 3 andTABLE 4 show the corresponding computed image digitizer modelparameters. More specifically, TABLE 3 shows gamma, gain and offsetvalues for the R, G, and B image digitizer channels, and TABLE 4 showsthe 3×3 mixing matrix M. Data was obtained from a Sharp® JX-450 imagedigitizer. FIG. 4 shows a graph of measured and predicted XYZtristimulus values for Macbeth® gray shades, plotted against imagedigitizer RGB values. Predictions were computed from least squaresvalues of gamma, gain, and offset values. FIG. 5 shows image digitizerXYZ measurements versus XYZ predictions for all Macbeth® colors.Predictions were computed from least squares values of gamma, gain,offset, and the mixing matrix M.

A second aspect of this invention, of primary importance, is the abilityto predict the color of colorants blended into an optically thicksubstrate. If colorants are mostly transparent, not very opaque, thenthey can be applied in layers and this invention still applies. Anillustrative non-limiting example of this latter case is the spraying oftextile dyes onto a carpet substrate. Layered colorants sometimesproduce colors that depend on the order of colorant application, butthis effect can be accommodated by this invention, and is describedlater in this Application.

In Kubelka-Munk Theory, the symbol R represents the fraction of lightreflected by a sample at a specific wavelength of light. In thisApplication, R generically denotes scaled versions of one of thetristimulus values, X, Y, or Z. As previously discussed, the tristimuluscoordinates X, Y, or Z represent averages over the red, green, and bluespectral bands, respectively. Therefore, our use of XYZ values for Rdiffers from Kubelka-Munk Theory. The chosen scaling of XYZ values mustproduce R values that are less than 1.

The ratio of light absorption and light scattering coefficients of acolorant mixture is denoted by K/S. K/S is dimensionless, and has threecomponents that correspond to the red, green, and blue spectral bands.K/S is related to R (the scaled XYZ values) by Equation 6.0. Equation6.0 comes from Kubelka-Munk Theory for an optically thick substrate.Equation 6.1 is the mathematical inverse of Equation 6.0. Equation 6.0is used for computing K/S when R is known by measurement. Equation 6.1is used for predicting R when K/S is known.

    K/S=(1-R).sup.2 /2R                                        Eq. 6.0

    R=(1+K/S)-[(1+K/S).sup.2 -1].sup.1/2                       Eq. 6.1

Equation 7.0 shows how absorption and scattering coefficients ofindividual colorants are combined in a mixture to produce K/S in thisApplication. The numerator of Equation 7.0 is a sum of light absorptionterms for each colorant in the mixture. The denominator is a sum oflight scattering terms for each colorant. N is the number of colorants.##EQU5##

K_(o) is the light absorption coefficient for a substrate withoutcolorants. The zero subscript denotes zero colorant concentration.Equation 8.0 below establishes the connection between R_(o) and K_(o).The reflectance of uncolored substrate is denoted by R_(o). Thisrelationship comes from Equation 7.0 when relative colorantconcentrations C_(i) and C_(j) are set to zero. This notation differssomewhat from standard colorimetric notation in that the substrate lightscattering coefficient S_(o) does not appear in Equation 7.0 Thesubstrate light scattering coefficient is factored into the othercoefficients in this Application, and explains why the dimensionlessterm "1" arises in the denominator of Equation 7.0 All light absorptionand scattering coefficients in this document are dimensionless becauseof this normalization.

The light absorption and light scattering coefficients K_(i) and S_(i)correspond to similar terms in the Kubelka-Munk Model. The lightabsorption blend coefficients for colorants i and j are denoted asK_(ij). We add these latter coefficients to the Kubelka-Munk Model inthis Invention to compensate for the fact that XYZ values are used inplace of spectral reflectivities at specific wavelengths. Thesecoefficients are generally not related to molecular interactions betweencolorants in the mixing media, although the coefficients mightcompensate for such interactions when they exist. If colorants areapplied in layers, then the ordering of the subscripts is important. Forexample, if colorant i is first applied to the substrate, followed bycolorant j, we use K_(ij). If colorant j is applied first, we useK_(ji). K_(ij) and K_(ji) are not generally equal.

Equation 7.1 comes from rearranging Equation 7.0 It is linear withrespect to colorant concentrations C_(i), and constitutes the basis forthe linear least squares fit calculations. Note K/S appears on bothsides of the equation. During the fit process, K/S is computed fromEquation 6.0 In all calculations, concentrations are expressed asfractions, not percentages. ##EQU6##

We now review the way that sample measurements are used to compute thelight absorption, scattering, and absorption blending coefficients. Thefirst step is to measure X, Y, Z values for uncolored substrate, denotedby numeral 170 in FIG. 6. See Step 1 in FIG. 7. When colorant is absentfrom the substrate, all colorant concentrations are zero, and we computeK_(o) from Equation 8.0 R_(o) represents scaled XYZ measurements of thesubstrate.

    (K/S).sub.o =K.sub.o =(1-R.sub.o).sup.2 /2R.sub.o          Eq. 8.0

When all colorants in a mixture are at very small concentrations, thisconstraint guarantees the predicted color of the substrate approachesthe color of uncolored substrate. This calculation is labeled 200 inFIG. 6. See STEP 2 in FIG. 7. Once calculated, K_(o) is used to computethe color of the substrate when colorant concentrations are exactlyzero.

The second step in this process is to obtain color measurements fromsamples made when one colorant is present at several concentrations.This is labeled 180 in FIG. 6. Because only one colorant is used, all ofthe K_(ij) C_(i) C_(j) terms in Equations 7.0 and 7.1 are zero. Let K₁and S₁ denote the light absorption and scattering coefficients forcolorant 1 at concentration C₁. K/S is calculated using Equations 6.0,and K_(o) is already known. We compute K₁ and S₁ using a least squaresfit as shown in Equations 9.0 through 9.5 ##EQU7##

Variable y denotes the dependent variable, and x₁ and x₂ denoteindependent variables. Variable w is a least squares weight forcingrelative errors to be uniform for XYZ predictions. Index q refers todifferent colorant concentrations, and P designates the total number ofdifferent colorant concentrations (the total number of samples). Thiscalculation is labeled 210 in FIG. 6. See STEP 3 in FIG. 7. Oncecalculated, K₁ and S₁ are used to predict color produced by differentconcentrations of colorant 1.

The third step of this process is to obtain color measurements ofsamples made with two colorants present at different concentrations. Lettwo colorants be labeled by subscripts 1 and 2. Both colorantconcentrations, C₁ are C₂, must be non-zero in the data set used for theleast squares fit. Total concentration, C₁ +C₂, must not exceed 100%. Itis best for these concentrations to span as wide a range as possible,and convenient (although not necessary) to choose C₁ +C₂ =100%. K_(o),K₁, S₁, K₂, and S₂ must already be known for colorants 1 and 2. Asusual, K/S is calculated using Equation 6.0. K₁₂ is to be determined.The step of measuring X, Y, Z values for substrates having pairs ofcolorants applied at several concentrations is denoted by numeral 190 inFIG. 6. ##EQU8## Index q refers to different colorant concentrations,and P designates the total number of pairs of blends (the total numberof samples). This calculation is labeled 220 in FIG. 6. See STEP 4 inFIG. 7. Once calculated, K₁₂ (along with K_(o), K₁, S₁, K₂, and S₂) isused to predict color produced by different blends of colorants 1 and 2.

The same procedure is used to determine parameters for other colorants.Once obtained, K_(o), K_(i), S_(i), and K_(ij) can be used to computeXYZ values for any colorant blend by utilizing equations 7.0 and 6.1This is the final step designated as 230 in FIG. 6.

The color of one colorant on a given substrate is defined by ninenumbers: K_(o), K₁, S₁. Two colorants on a given substrate have colordefined by eighteen numbers: K_(o), K₁, S₁, K₂, S₂, K₁₂. (We exclude thecase where K₂₁ is necessary as discussed earlier in this Application.)The color of three colorants on a given substrate is defined by thirtynumbers: K_(o), K₁, S₁, K₂, S₂, K₃, S₃, K₁₂, K₁₃, K₂₃. Thesecoefficients summarize all sample measurements, and would normally besaved in a computer database for subsequent blend calculations; e.g., 7in FIG. 1.

One application for this type of colorant blending analysis is theapplication of dyes to a carpet substrate using computer controlled dyejet technology. This is not to be construed as limiting in any way,since any optically thick substrate can be utilized with this process.Measurements must be made after the carpet is in final product form;e.g., after the carpet dye (if any) is fixed, after shearing, aftertopical treatments are applied, and so on. This requirement includesmeasurements made of undyed samples used to compute K_(o) for the carpetsubstrate. If a colorimeter is used instead of an image digitizer, it ispreferable to limit measurements to one colorimeter. If the colorimeterprovides CIE L*a*b* measurements, these color coordinates must beconverted into XYZ tristimulus values using the appropriate colorimetricequations. The colorimeter must be calibrated using the largest possibleaperture, preferably at least 2" in diameter. Glass is not used on thecolorimeter aperture because crushing the carpet pile against glass addsa gloss that is not observed on carpet during normal use. Carpet pile onsamples is manually set before measurement so it lies in its preferreddirection.

FIG. 7 consists of four graphical embodiments entitled STAGED REGRESSIONSTEPS FOR DYE BLEND CALCULATIONS. It is a graphic representation of thecalculations required to obtain colorant light absorption, scattering,and blending coefficients. The example assumes that the blendedcolorants consist of two dyes applied to a textile substrate. Dyes 1 and2 are blended at relative concentrations C₁ and C₂, respectively. C₁, C₂and R are depicted by coordinate axes at right angles.

Refer to STEP 1 of FIG. 7. As stated earlier, it is computationallysimpler to use the ratio K/S rather than R. The mathematical connectionbetween K/S and R is shown in Step 1 of FIG. 7. All calculatedpredictions are obtained from measurements of undyed or dyed samples.One sample must have no colorant applied (C₁ =C₂ =0), and is the pointlabeled "No Dye". This point has the lightest measured color, so themeasurement is shown as the data point highest in the R direction.

Several samples must have different amounts of Dye 1. These are thepoints labeled "33% Dye 1", "66% Dye 1", and "100% Dye 1", and all liein the plane formed by the C₁ and R axes. These points are lower(darker) then the "No Dye" measurement. The greater the amount of Dye 1,the closer (darker) the measurements move towards the C₁ axis. Similarstatements can be made for the samples with different amounts of Dye 2.In this example, measurements of R for Dye 2 are smaller than for Dye 1.This means Dye 1 is lighter in color than Dye 2 for color component R.

STEP 1 also shows three measurements with different blends of Dyes 1 and2. Only one measurement is labeled, "50% Dye 1+50% Dye 2". A dashed linelies in the plane formed by the C₁ and C₂ axes. The points on this linesatisfy the equation C₁ +C₂ =100%. It is convenient to prepare blendsamples so this equation is satisfied. The three two-dye blend colorsshown in the drawing satisfy this relationship, and therefore lie abovethe dashed line in this three dimensional space. For example, the othertwo points can be "33% Dye 1+67% Dye 2" and "67% Dye 1+33% Dye 2". Thesum of the blend concentrations is then 100% for both dye blends.

In summary, if we viewed the coordinate system in the drawing down alongthe R axis, then the one-dye measurements would be projected onto the C₁or C₂ axes, and the two-dye blend measurements would be projected ontothe dashed line crossing the C₁ and C₂ axes. Arbitrary blends satisfyingthe constraint C₁ +C₂ ≦100% would fall inside the triangle formed bythese three lines.

Refer to STEP 2 of FIG. 7. The first stage in the series of regressionsuses samples without colorants to compute K_(o). A 100% wet out solutionwithout colorant must sometimes be applied to uncolored substrates (suchas greige textile fabric), and be processed as part of (mix blanketsamples, if it imparts any color or otherwise alters appearance. This"clear" solution is sometimes used to blend colorants on a substrate. Itwould therefore be used during the creation of the colorant dilution andbinary colorant blend samples.

Zero colorant sample measurements are used to compute the lightabsorption coefficient for the substrate, K_(o). If we stop ourcalculations at this point, and use K/S-K_(o) to predict colors forblends of Dye 1 and 2, the predictions would only match the measurementwhen C₁ =C₂ -0. Predictions are denoted in Step 2 of FIG. 7 by thetriangular plane of predictions intersecting the "No Dye" point. In thisfirst stage of the regression, only the "No Dye" prediction matches themeasurements.

Refer to STEP 3 in FIG. 7. This step uses colored samples to compute K₁,S₁, K₂, and S₂. It is recommended that each colorant have at least fivedifferent concentrations, although only three are shown in FIG. 7. 0%concentration is not used in this step, but it should include 100%concentration. One possible set is 15%, 20%, 30%, 50%, and 100%. Thechoice of uneven concentration increments is more likely to produce avisually uniform color gradient. Small amounts of colorant have a strongimpact on final color. If ten different concentrations can beaccommodated, a possible set is 15%, 20%, 25%, 30%, 35%, 40%, 50%, 60%,80%, and 100%.

Single colorant dilution measurements are used to compute lightabsorption and scattering coefficients. These new terms are added to theformula for K/S, as shown in STEP 3. Also shown as solid lines is thenew prediction surface. The new predictions lie close to the single dyemeasurements. They do not match perfectly because the calculation is aleast squares fit. Goodness of fit are limited by measurement precision,and by degrees of freedom in our mathematical model. Note the predictionstill matches the "No Dye" measurement. The second stage of regressiondoes not disturb the first stage of regression. However, the predictionsurface still does not match the dye blend measurements satisfactorily.

Refer to STEP 4 of FIG. 7. The final step uses pairs of colorants toestablish K_(ij). It is recommended that each colorant have at leastfive different concentrations, although only three are shown in FIG. 7.0% and 100% concentrations must not be used. One possible set is15%/85%, 33%/67%, 50%/50%, 67%/33%, and 85%/15%. If ten differentconcentrations can be accommodated, one possible set is 15%/85%,20%/80%, 25%/75%, 30%/70%, 40%/60%, 60%/40%, 70%/30%, 75%/25%, 80%/20%,and 85%/15%. The choice of uneven concentration increment is more likelyto produce a visually uniform color gradient. Small amounts of coloranthave a strong impact on final color.

Colorant pair blending measurements are used to compute light absorptionblending coefficients. This adds one more term to the formula for K/S,as shown in STEP 4. Now the prediction curve satisfactorily predicts allof the dye measurements. Again, the final predictions do not matchperfectly because the calculation is a least squares fit. This thirdregression stage has no effect on no-dye or dye pair blendingpredictions.

In summary, the modified Kubelka-Munk Model is fit to measurements instages, each successive stage including more measurement data, andfurther reducing the total least squares error. The accuracy of priorpredictions are not affected. The algebraic reason for this decouplingis that each expression for the numerator K and denominator S in theequation for K/S contains increasingly higher ordered products ofcolorant concentrations. If both colorant concentrations are zero, allterms with C₁, C₂, and C₁ *C₂ vanish. The only term left is the oneshown in STEP 2. If one colorant concentration is zero, terms with C₁*C₂ vanish. The only terms left are ones shown in STEP 3. Only when bothconcentrations are non-zero, so that the C₁ *C₂ term is present, doesall of the terms shown in STEP 4 apply.

Predictions of colorant blends fall on the curved surface shown in STEP4 of the drawing. Predictions are satisfactory for our specifiedapplications over the entire surface. Arbitrary predictions areinterpolations based on the K/S model, made with the shown formula (thesame as Equation 7.0). When three colorants are involved, theinterpolation region is a volume, and so on. While this mathematicalprocess can be extended to higher order terms (e.g., S₁₂, K₁₂₃, S₁₂₃,and so on), we find this is unnecessary for tristimulus coordinateprediction.

The addition of a third colorant does not affect the values of K₀, K₁,S₁, K₂, S₂, or K₁₂. But we must compute coefficients K₃, S₃, K₁₃, andK₂₃, if predictions are desired for blends involving the third colorant.Again, all of the prior predictions for blends of Dye 1 and Dye 2 remainunaffected, even though extra terms are added to the K/S equation.

TABLE 5 through TABLE 7 show a lists of light absorption, lightscattering, and light absorption blend coefficients for seven textiledyes. These dyes were applied to carpet substrates by spraying the dyesunder computer control. There are three dark dyes ("deep"), three mediumdyes ("pale"), and one light dye (yellow). Blend predictions for asubset of four dyes (pale red, pale green, pale blue and yellow), areshown in TABLE 8 through TABLE 11.

The third and final aspect of this Invention is to display thecalculated blend colors on an RGB based electronic display. It is commonfor computerized design systems to display colors on cathode ray tubes(CRTs). Any electronic display using RGB values, such as liquid crystaldisplays, among others, can be employed for the purposes of thisApplication. Cathode ray tubes (CRTs) emit light in three primarycolors. This excites the red, green and blue receptors in the humanretina. For convenience, we refer to CRT displays in this Application,although any RGB based electronic display can be used such as anelectroluminiscent display or a plasma display. Colors emitted byelectronic displays are measured by a radiometers or chroma meters(e.g., Minolta® TV-Color Analyzer II, Minolta® CRT Color AnalyzerCA-100, Minolta® Chroma Meter CS-100). Of the various color coordinatesavailable from color measurement devices, as previously stated, XYZtristimulus values are chosen in this Application.

XYZ values measured from devices that emit light have dimensions; e.g.,candelas per square meter. These measurements are said to be absolute.Relative XYZ values will now be denoted X'Y'Z'. These values aredimensionless, and usually expressed as a percentage. Different absolutemeasurements for the same white media (having the same chromaticity) areusually scaled to the same relative values for electronic visual displayor computer imaging hardcopy applications. The maximum Y value possiblefor a display device is sometimes chosen to convert absolute XYZmeasurements into relative X'Y'Z' values. For example, if the maximum Yvalue possible for a CRT is 80 cd/m², and one displayed color measuresX=60 cd/m², Y=70 cd/m², Z=75 cd/m², then the corresponding relativeX'Y'Z' values are X'=75.00, Y'=87.50, and Z'=93.75. Although these arepercentages, the percent sign is customarily omitted.

As discussed earlier in this Application, it is common for colormeasurements to be expressed in terms of chromaticity x and y, and"luminance" Y. Conversion between XYZ values to xyY values isaccomplished as described earlier in this Application. Note that thedimensioned values of X and Y are thereby converted into dimensionlessvalues of x and y. The chromaticity range of a typical CRT color monitorused for computer aided design is shown in FIG. 3, and compared withchromaticities of Macbeth® ColorChecker® colors.

Current electronic color displays do not use XYZ values directly todisplay colors. Such devices commonly use RGB values, indicating thestrength of red, green, and blue phosphor light emission. Red, green,and blue color components are denoted as R, G, and B, respectively. RGBvalues commonly range from 0 through 255. We show how to convert fromabsolute XYZ tristimulus values to RGB electronic display values. FIG. 1shows a CRT display as 4, that accepts and returns a color as RGBvalues. Conversion between XYZ and RGB values is performed by 6 in FIG.1, a CRT Model Algorithm.

In phase one of the computations, separate measurements are made of thered, green, and blue CRT phosphors at different brightnesses. This mustbe done for several levels of RGB values. A typical set of RGB valuesfor the phosphor measurements are 50, 100, 150, 200, 225, and 255. It ispreferable to include the smallest RGB value that provides a dependablemeasurement. This is about Y=0.6 cd/m² for the Minolta® TV-ColorAnalyzer II, and about Y=0.3 cd/m² for the Minolta® CRT Color AnalyzerCA-100. This data collection step is numeral 260 in FIG. 8. In thisdocument, RGB and XYZ values are normalized so values fall mostlybetween 0 and 1. This step is denoted in FIG. 8 by numeral 270. Thesemeasurements are used to compute model parameters that arecharacteristic of the red, green, and phosphors. In phase two of thecomputations, a mixing matrix is computed so any color can be converted,not just colors produced when one phosphor is on.

Earlier in this Application the Image Digitizer Model Algorithm (5 inFIG. 1) was described. The CRT Model Algorithm (6 in FIG. 1) forelectronic color display is very similar. In fact, the CRT ModelAlgorithm came first and was adapted for digitizer color measurement tocreate the Digitizer Model Algorithm for this Invention. The terminologyused in the CRT Model Algorithm (e.g., gamma, gain, offset) areassociated with the internal electronics of a CRT; e.g., electron beamintensity and amplifier voltages. As this Application demonstrates, themathematical aspects of the model can be adapted to RGB based devicessuch as image digitizers and other kinds of electronic color displaydevices.

Tristimulus values for red, green, and blue CRT phosphors are denoted byX_(r), Y_(g), and Z_(b), respectively, and are generically referred toas X_(r) Y_(g) Z_(b) values. X_(r) is the X value measured when only thered phosphor is turned on (G and B are zero), Y_(g) is the Y valuemeasured when only the green phosphor is turned on (R and B are zero),and Z_(b) is the Z value measured when only the blue phosphor is turnedon (R and G are zero).

For a CRT, gamma is the parameter that characterizes the nonlinearrelationship between the electron beam acceleration voltage and theresulting color brightness. Gamma values for the red, green and bluephosphors are denoted as g_(r), g_(g), and g_(b), respectively. Theseare collectively referred to as "gamma" or g.

For a CRT, gain is the parameter that characterizes the perceivedcontrast level of resulting colors. Gain values for the red, green andblue phosphors are denoted as G_(r), G_(g), and G_(b), respectively.These are collectively referred to as "gain" or G.

For a CRT, offset if the parameter that characterizes the perceivedbrightness of resulting colors. Offset values for the red, green andblue phosphors are denoted as O_(r), O_(g), and O_(b), respectively.These are collectively referred to as "offset" or O.

Gain, offset and gamma parameters in the CRT Model Algorithm define aquantitative relationship between measured color (absolute XYZtristimulus values) and CRT color coordinates color components (RGBvalues) for each CRT phosphor. This is shown in the following equations.You will notice these equations are identical to those presented earlierin this Application for the Image Digitizer Model Algorithm.

    X.sub.r =(G.sub.r +O.sub.r *R).sup.gr                      Eq. 1.0

    Y.sub.g =(G.sub.g +O.sub.g *G).sup.gg                      Eq. 1.1

    Z.sub.b =(G.sub.b +O.sub.b *B).sup.gb                      Eq. 1.2

We now explain how to compute the CRT model parameters from the colorphosphor measurements. X_(r) is measured when only the red phosphor isturned on (G and B are zero), Y_(g) is measured when only the greenphosphor is turned on (R and B are zero), and Z_(b) is measured whenonly the blue phosphor is turned on (R and G are zero). The first stepis to chose either the red, green or blue phosphor for furthercomputation as designated by numeral 280 in FIG. 8. Equations 1.0, 1.1and 1.2 are in the following form (x and y are not chromaticityvariables):

    y=(G+O*x).sup.g                                            Eq. 2.0

Equation 2.0 can be rewritten as an equation linear in y^(1/g). That is,a graph of x as a function of y^(1/g) is a straight line.

    y.sup.1/g =G+O*x                                           Eq. 2.1

For specific values of g, G, and O, we define a least squares error E. Asubscript m denotes individual measurements x_(m) (representing R_(m) orG_(m) or B_(m)) and y_(m) ^(1/g) (representing X_(rm) ^(1/gr) or Y_(gm)^(1/gg) or Z_(bm) ^(1/gb)) There is a total of N measurements for aphosphor, so m ranges from 1 to N. The number of measurements perphosphor need not be the same. ##EQU9## For computational purposes, anexpanded form of Equation 2.2 is preferred. Equation 2.3 is expressed interms of summations that will already exist in prior computational stepsin the final algorithm.

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S                                                Eq. 2.3

The following summation equations determine the "S" variable values:##EQU10## The variable S in Equation 2.4 is equal to the number ofphosphor measurements. Equation 2.1 is nonlinear in g. Because of thisnonlinearity, our approach is not to minimize the least squares errorfound in Equation 2.3 for g, G, and O simultaneously. Instead, we pick areasonable value for g (290 in FIG. 8) and find G and O that minimizethe least squares error (300 in FIG. 8). For this g, G and O are givenby Equations 3.0, 3.1, and 3.2. These Equations are solutions to theleast squares fit for a given value of g.

    D=S.sub.xx S-S.sub.x.sup.2                                 Eq. 3.0

    G=(S.sub.xx S.sub.y -S.sub.x S.sub.xy)/D                   Eq. 3.1

    O=(-S.sub.x S.sub.y +S S.sub.xy)/D                         Eq. 3.2

Our chosen g and the computed optimal values for G and O can be put intoEquation 2.3 to compute the least squares error E (or E²) as designatedby numeral 310 in FIG. 8. We then can pick another value of g, whichallows us to compute another set of optimal values of G and O, that inturn gives a new least squares error. This step is designated by numeral320 in FIG. 8. For two estimates of g, the better value is the onegiving the smaller least squares error E (or E²). The least squareserror E is not sensitive to changes in gamma g by differences of 0.25The algorithm chooses values of g from 1 through 5 in increments of 0.25As outlined above, for each g, compute G and O from Equations 2.4through 2.9, and 3.0 through 3.2, and least squares error E² fromEquation 2.3 The best value of g is the one minimizing E². This finalselection of g is designated by numeral 330 in FIG. 8.

As previously stated with regard to numeral 280 of the flowchart in FIG.8, this calculation is repeated separately for the red, green, and bluecomponents of the corresponding measured phosphor colors. This step isdesignated by numeral 340 in FIG. 8, which will repeat steps 290, 300,310, 320, and 330 in FIG. 8 for each CRT phosphor.

Once gamma, gain, and offset parameters are computed, Equation 1.0predicts X_(r), from R, when G and B are zero, with minimized error. Andso on for the green and blue phosphors (only one phosphor on, the othertwo off). Equations 1.0, 1.1, and 1.2 do not by themselves accuratelypredict arbitrary colors.

The next step is to use all of the phosphor measurements to convert RGBvalues of arbitrary colors into XYZ values (or vice versa). One ofGrassman's Laws provides an approximate way to calculate tristimulusvalues for arbitrary colors. It is applicable because CRT monitorscreates colors by additive color mixing. A mixing matrix M produces alinear combination of the phosphor tristimulus values. Define the columnmatrix of measured tristimulus coordinates for any color as: ##EQU11##and the column matrix of predicted XYZ values computed from Equations1.0, 1.1 and 1.2, as: ##EQU12## Then X and X_(rgb) are connected by thelinear relationship

    X=MX.sub.rgb                                               Eq. 4.2

where M is a 3×3 matrix. M is computed from all of the measurements usedto compute the gain, offset and gamma parameters, in a least squares(pseudo-inverse) fashion, as follows. Define a 3×3N matrix Q whosecolumns are the 3N phosphor measurements X_(m) of the kind defined inEquation 4.0 Recall there are N measurements each for red, green, andblue phosphors, hence there are 3N columns to the matrix.

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |Eq. 4.3

Also define a 3×3N matrix Q_(rgb) containing the correspondingpredictions obtained from Equations 1.0, 1.1 and 1.2 for the same 3Nmeasurements.

    Q.sub.rgb =|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . Z.sub.rgbN |                                                Eq. 4.4

The computation of Q and Q_(rgb) from XYZ measurements and predictionsof all phosphor color measurements is designated as numeral 350 in FIG.8. The columns of Q and Q_(rgb) are connected by matrix M in Equation4.2, so therefore:

    Q=MQ.sub.rgb                                               Eq. 4.5

This holds true if the CRT model (Equations 1.0, 1.1, and 1.2) isexactly true and color measurements are without error. The model anddata are not exact, so the "best" (least squares) solution is obtainedby solving Equation 4.5 using a pseudo-inverse as follows:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1                      Eq. 4.6

Superscript T denotes matrix transpose, and superscript -1 denotesmatrix inverse. This step is designated by numeral 360 in FIG. 8. Theinverse is performed on a 3×3 matrix. Once the gain, offset, gamma, andmixing matrix M are known, Equations 1.0, 1.1, 1.2 and 4.2 are used toconvert CRT R, G, and B into X, Y, and Z for any color. The inversetransformation, converting X, Y, and Z into R, G, and B, is computed asfollows:

    X.sub.rgb =M.sup.-1 X                                      Eq. 5.0

    R=(X.sub.r.sup.1/gr -G.sub.r)/O.sub.r                      Eq. 5.1

    G=(Y.sub.g.sup.1/gg -G.sub.g)/O.sub.g                      Eq. 5.2

    B=(Z.sub.b.sup.1/gb -G.sub.b)/O.sub.b                      Eq. 5.3

FIG. 9 shows a graph of CRT model calculations for red, green and bluephosphors for a typical CRT used for computer aided design. XYZtristimulus values are plotted against RGB values. FIG. 10 shows CRTmeasurements versus predictions for all phosphor colors. XYZ predictionsare plotted against XYZ measurements.

We now have the means to convert between absolute color measurements(XYZ tristimulus values), and electronic color display components (RGBvalues). A conversion between absolute color measurements (XYZtristimulus values), and relative color measurements (X'Y'Z' tristimulusvalues), is also necessary. There are subtle issues in reproducingcolors on an electronic display involving human color vision that arenot addressed here. And, to avoid discussing these issues we adopt alinear relationship between XYZ and X'Y'Z'. In matrix notation

    X=W(X'-B)                                                  Eq. 11.0

    X'=(X/W)+B                                                 Eq. 11.1

where W and B are scalars. Scalars are used so the red, green, and bluecolor components are identically weighted. W and B adjust levels oflight and dark colors, respectively. X and X' are three component columnmatrices representing XYZ and X'Y'Z', respectively.

When B=0%, colors are usually perceived to be washed out on typical CRTcolor displays, and black is not dark enough. Increasing B improvescolor contrast. We find B=2% gives best results. If necessary, B can bea negative number, and W can be greater than one. W can be calculated socomputed RGB values never exceed their limit, usually values of 255. Bychoosing a suitable white standard (for example, white in the Macbeth®ColorChecker® color set), and comparing these relative X'Y'Z values tothe absolute XYZ values obtained with a CRT when RGB values are at theirmaximum level, Equation 11.0 can be use to compute W. (Explicit formulascan be derived for this purpose.) This allows the full range of CRTluminance to be used for displaying colors. W is responsible forconverting absolute color measurements XYZ to relative colormeasurements X'Y'Z', and is therefore not dimensionless. The selectionor computation of brightness W and contrast B is designated by numeral370 in FIG. 8.

We now have the means to convert between relative color measurements(X'Y'Z' tristimulus values) obtained from color measurement equipment,and computer color components (RGB values). This step is designated bynumeral 380 in FIG. 8. This is also shown in FIG. 1 as the retrieval ofXYZ data from the XYZ COLOR DATABASE 7, performing the above operationsusing the CRT MODEL ALGORITHM 6, and then displaying the RGB values onthe CRT DISPLAY 4. Furthermore, RGB values obtained from the CRT DISPLAY4, can be transformed into XYZ coordinates by the CRT MODEL ALGORITHM 6,and then sent back to the XYZ COLOR DATABASE 7.

It is not intended that the scope of the invention be limited to thespecific embodiments illustrated and described. Rather, it is intendedthat the scope of the invention be defined by the appended claims andtheir equivalents.

                  TABLE 1                                                         ______________________________________                                        NO.  NAME        x      y    Y     X    Y    Z                                ______________________________________                                         1   Dark Skin   0.400  0.350                                                                              10.1  11.54                                                                              10.10                                                                              7.21                              2   Light Skin  0.377  0.345                                                                              35.8  39.12                                                                              35.80                                                                              28.85                             3   Blue Sky    0.247  0.251                                                                              19.3  18.99                                                                              19.30                                                                              38.60                             4   Foliage     0.337  0.422                                                                              13.3  10.62                                                                              13.30                                                                              7.60                              5   Blue Flower 0.265  0.240                                                                              24.3  26.83                                                                              24.30                                                                              50.12                             6   Bluish Green                                                                              0.261  0.343                                                                              43.1  32.80                                                                              43.10                                                                              49.76                             7   Orange      0.506  0.407                                                                              30.1  37.42                                                                              30.10                                                                              6.43                              8   Purplish Blue                                                                             0.211  0.175                                                                              12.0  14.47                                                                              12.00                                                                              42.10                             9   Moderate Red                                                                              0.453  0.306                                                                              19.8  29.31                                                                              19.80                                                                              15.59                            10   Purple      0.285  0.202                                                                              6.6   9.31 6.60 16.76                            11   Yellow Green                                                                              0.380  0.489                                                                              44.3  34.43                                                                              44.30                                                                              11.87                            12   Orange Yellow                                                                             0.473  0.438                                                                              43.1  46.54                                                                              43.10                                                                              8.76                             13   Blue        0.187  0.129                                                                              6.1   8.84 6.10 32.34                            14   Green       0.305  0.478                                                                              23.4  14.93                                                                              23.40                                                                              10.62                            15   Red         0.539  0.313                                                                              12.0  20.66                                                                              12.00                                                                              5.67                             16   Yellow      0.448  0.470                                                                              59.1  56.33                                                                              59.10                                                                              10.31                            17   Magenta     0.364  0.233                                                                              19.8  30.93                                                                              19.80                                                                              34.25                            18   Cyan        0.196  0.252                                                                              19.8  15.40                                                                              19.80                                                                              43.37                            19   White       0.310  0.316                                                                              90.0  88.29                                                                              90.00                                                                              106.52                           20   Neutral 8.0 0.310  0.316                                                                              59.1  57.98                                                                              59.10                                                                              69.95                            21   Neutral 6.5 0.310  0.316                                                                              36.2  35.51                                                                              36.20                                                                              42.84                            22   Neutral 5.0 0.310  0.316                                                                              19.8  19.42                                                                              19.80                                                                              23.43                            23   Neutral 3.5 0.310  0.316                                                                              9.0   8.83 9.00 10.65                            24   Black       0.310  0.316                                                                              3.1   3.04 3.10 3.67                             ______________________________________                                    

                  TABLE 2                                                         ______________________________________                                        NO.  NAME        X      Y     Z     R    G    B                               ______________________________________                                         1   Dark Skin   11.54  10.10 7.21  110   70   62                              2   Light Skin  39.12  35.80 28.85 190  142  135                              3   Blue Sky    18.99  19.30 38.60  99  119  158                              4   Foliage     10.62  13.30 7.60   84   91   64                              5   Blue Flower 26.83  24.30 50.12 133  128  179                              6   Bluish Green                                                                              32.80  43.10 49.76 128  181  174                              7   Orange      37.42  30.10 6.43  192  110   69                              8   Purplish Blue                                                                             14.47  12.00 42.10  86   92  168                              9   Moderate Red                                                                              29.31  19.80 15.59 181   88  105                             10   Purple      9.31   6.60  16.76  90   64  106                             11   Yellow Green                                                                              34.43  44.30 11.87 150  170   88                             12   Orange Yellow                                                                             46.54  43.10 8.76  203  146   80                             13   Blue        8.84   6.10  32.34  63   64  157                             14   Green       14.93  23.40 10.62  87  135   88                             15   Red         20.66  12.00 5.67  173   63   64                             16   Yellow      56.33  59.10 10.31 221  186   82                             17   Magenta     30.93  19.80 34.25 183   96  151                             18   Cyan        15.40  19.80 43.37  80  126  165                             19   White       88.29  90.00 106.52                                                                              250  249  253                             20   Neutral 8.0 57.98  59.10 69.95 197  199  215                             21   Neutral 6.5 35.51  36.20 42.84 154  153  169                             22   Neutral 5.0 19.42  19.80 23.43 116  114  127                             23   Neutral 3.5 8.83   9.00  10.65  80   70   88                             24   Black       3.04   3.10  3.67   39   34   43                             ______________________________________                                    

                  TABLE 3                                                         ______________________________________                                        COMPUTED IMAGE DIGITIZER                                                      MODEL PARAMETERS                                                              gamma             gain    offset                                              ______________________________________                                        R      2.00           0.0169  0.9480                                          G      2.25           0.0985  0.8825                                          B      2.75           0.1492  0.8760                                          ______________________________________                                    

                  TABLE 4                                                         ______________________________________                                        COMPUTED IMAGE DIGITIZER MODEL PARAMETERS                                     ______________________________________                                         ##STR1##                                                                     ______________________________________                                    

                  TABLE 5                                                         ______________________________________                                        K.sub.ox        K.sub.oy                                                                              K.sub.oz                                              ______________________________________                                        0.09328         0.06876 0.06218                                               ______________________________________                                    

                                      TABLE 6                                     __________________________________________________________________________    DYE NO.                                                                             DYE NAME                                                                             K.sub.x                                                                           K.sub.y                                                                           K.sub.z                                                                           S.sub.x                                                                           S.sub.y                                                                           S.sub.z                                      __________________________________________________________________________    1     Deep Red                                                                             16.2549                                                                           32.8022                                                                           74.9094                                                                           2.5897                                                                            2.2356                                                                            0.0515                                       2     Deep Green                                                                           14.7451                                                                            9.7676                                                                           10.2859                                                                           0.3686                                                                            0.4831                                                                            0.3583                                       3     Deep Blue                                                                            12.7319                                                                           10.4875                                                                            3.0545                                                                           0.8023                                                                            0.6334                                                                            0.7765                                       4     Pale Red                                                                              1.8067                                                                            2.0707                                                                            3.1958                                                                           1.6599                                                                            1.4389                                                                            1.2618                                       5     Pale Green                                                                            2.3385                                                                            1.9950                                                                            4.1897                                                                           0.9957                                                                            0.9260                                                                            1.0124                                       6     Pale Blue                                                                             3.0687                                                                            2.4645                                                                            1.7175                                                                           0.6789                                                                            0.6329                                                                            0.6966                                       7     Yellow  0.8954                                                                            0.7291                                                                            3.2458                                                                           1.9394                                                                            1.3345                                                                            0.8841                                       __________________________________________________________________________

                  TABLE 7                                                         ______________________________________                                        Dye  Dye                                                                      No.  No.     Dye                                                              i    j       Blend       K.sub.ijx                                                                            K.sub.ijy                                                                             K.sub.ijz                             ______________________________________                                        1    2       Deep Red +  142.4729                                                                             199.4130                                                                              63.1336                                            Deep Green                                                       1    3       Deep Red +  189.8662                                                                             252.6969                                                                              133.5376                                           Deep Blue                                                        2    3       Deep Green +                                                                              21.6591                                                                              13.2452 9.8802                                             Deep Blue                                                        4    5       Pale Red +  3.1668 2.6439  4.5439                                             Pale Green                                                       4    6       Pale Red +  7.2048 5.1524  2.1763                                             Pale Blue                                                        5    6       Pale Green +                                                                              4.3949 3.2950  1.5603                                             Pale Blue                                                        4    7       Pale Red +  2.1295 2.0346  6.9012                                             Yellow                                                           5    7       Pale Green +                                                                              2.8697 1.7687  4.4579                                             Yellow                                                           6    7       Pale Blue + 3.9054 1.6108  1.4522                                             Yellow                                                           4    3       Pale Red +  13.7953                                                                              7.9671  1.5650                                             Deep Blue                                                        7    3       Yellow +    21.3027                                                                              8.4927  3.4470                                             Deep Blue                                                        ______________________________________                                    

                  TABLE 8                                                         ______________________________________                                        GREIGE DATA: White                                                            X.sub.o                                                                              Y.sub.o  Z.sub.o                                                                              K.sub.ox K.sub.oy                                                                            K.sub.oz                                ______________________________________                                        65.14  69.16    70.41  0.0933   0.0688                                                                              0.0622                                  ______________________________________                                    

                  TABLE 9                                                         ______________________________________                                        DYES TO BLEND: Pale Red + Pale Green +                                        Pale Blue + Yellow                                                            Dye                                                                           No.   K.sub.x K.sub.y  K.sub.z                                                                             S.sub.x                                                                              S.sub.y                                                                             S.sub.z                             ______________________________________                                        4     1.8067  2.0707   3.1958                                                                              1.6599 1.4389                                                                              1.2618                              5     2.3385  1.9950   4.1897                                                                              0.9957 0.9260                                                                              1.0124                              6     3.0687  2.4645   1.7175                                                                              0.6789 0.6329                                                                              0.6966                              7     0.8954  0.7291   3.2458                                                                              1.9394 1.3345                                                                              0.8841                              ______________________________________                                    

                  TABLE 10                                                        ______________________________________                                        DYE                                                                           NUMBERS    K.sub.IJX    K.sub.IJY                                                                             K.sub.IJZ                                     ______________________________________                                        4 + 5      3.1668       2.6439  4.5439                                        4 + 6      7.2048       5.1524  2.1763                                        5 + 6      4.3949       3.2950  1.5603                                        4 + 7      2.1295       2.0346  6.9012                                        5 + 7      2.8697       1.7687  4.4579                                        6 + 7      3.9054       1.6108  1.4522                                        ______________________________________                                    

                  TABLE 11                                                        ______________________________________                                        BLEND COLOR                                                                   C.sub.1                                                                           C.sub.2                                                                             C.sub.3                                                                              C.sub.4                                                                           (K/S).sub.x                                                                         (K/S).sub.y                                                                         (K/S).sub.z                                                                         X     Y    Z                           ______________________________________                                        0.0 0.0   0.0    0.0 0.0933                                                                              0.0688                                                                              0.0622                                                                              65.14 69.16                                                                              70.41                       0.0 0.0   0.0    0.1 0.1531                                                                              0.1250                                                                              0.3553                                                                              57.89 60.96                                                                              44.05                       0.0 0.0   0.1    0.2 0.4515                                                                              0.3708                                                                              0.7318                                                                              39.94 43.32                                                                              31.79                       0.0 0.1   0.2    0.3 0.8903                                                                              0.7382                                                                              1.3617                                                                              28.62 31.65                                                                              22.22                       0.1 0.2   0.3    0.4 1.4276                                                                              1.2311                                                                              2.1626                                                                              21.55 23.67                                                                              16.23                       0.2 0.3   0.4    0.3 1.9326                                                                              1.6794                                                                              2.4965                                                                              17.58 19.36                                                                              14.61                       0.3 0.4   0.3    0.2 1.9366                                                                              1.7309                                                                              2.6033                                                                              17.55 18.97                                                                              14.15                       0.4 0.3   0.2    0.1 1.6098                                                                              1.4929                                                                              2.2185                                                                              19.92 20.94                                                                              15.93                       0.3 0.2   0.1    0.0 1.0787                                                                              1.0205                                                                              1.4538                                                                              25.63 26.48                                                                              21.30                       0.2 0.1   0.0    0.0 0.5252                                                                              0.5327                                                                              0.8948                                                                              37.36 37.12                                                                              28.54                       0.1 0.0   0.0    0.0 0.2349                                                                              0.2411                                                                              0.3390                                                                              51.03 50.60                                                                              44.85                       ______________________________________                                    

                  TABLE 12                                                        ______________________________________                                        CRT MEASUREMENTS                                                              R      G          B      Y        x    y                                      ______________________________________                                        225     0          0     23.30    0.630                                                                              0.336                                  225     0          0     17.30    0.630                                                                              0.336                                  200     0          0     13.00    0.630                                                                              0.336                                  150     0          0     6.35     0.630                                                                              0.336                                  100     0          0     2.28     0.628                                                                              0.336                                   50     0          0     0.36     0.611                                                                              0.335                                   0     255         0     75.50    0.270                                                                              0.608                                   0     225         0     56.00    0.270                                                                              0.609                                   0     200         0     42.50    0.271                                                                              0.609                                   0     150         0     21.30    0.272                                                                              0.609                                   0     100         0     7.88     0.272                                                                              0.609                                   0      50         0     1.30     0.273                                                                              0.602                                   0      40         0     0.71     0.273                                                                              0.596                                   0      30         0     0.32     0.273                                                                              0.578                                   0      0         255    9.50     0.143                                                                              0.057                                   0      0         225    7.10     0.143                                                                              0.057                                   0      0         200    5.35     0.143                                                                              0.057                                   0      0         150    2.67     0.143                                                                              0.057                                   0      0         100    0.97     0.143                                                                              0.058                                   0      0          80    0.55     0.143                                                                              0.058                                   0      0          60    0.26     0.144                                                                              0.060                                  ______________________________________                                         High Resolution Sony ® Monitor using a Minolta ® CA100           

                  TABLE 13                                                        ______________________________________                                        COMPUTED CRT MODEL PARAMETERS                                                 gamma            gain     offset                                              ______________________________________                                        R      2.25          -0.0384  0.7297                                          G      2.25          -0.0327  0.9134                                          B      2.25          -0.0579  1.1958                                          ______________________________________                                    

                  TABLE 14                                                        ______________________________________                                        COMPUTED CRT MODEL PARAMETERS                                                 ______________________________________                                         ##STR2##                                                                     ______________________________________                                    

What is claimed is:
 1. A process for scanning RGB values of a sampleutilizing an image digitizer and converting said RGB values of saidsample to XYZ values comprising the steps of:(a) scanning a color targetchart having gray shades with same chromaticities with an imagedigitizer to collect RGB target color values; (b) scanning said colortarget chart having gray shades with same chromaticities to collect XYZtarget tristimulus color values with a colorimeter; (c) normalizing saidRGB target color values and said XYZ target tristimulus color values;(d) picking a value of gamma (g) for an X tristimulus color value ofsaid target gray shades; (e) computing a least squares fit for saidpicked value of gamma (g) with following formulas: ##EQU13## N=Totalnumber of gray shade measurements m=individual gray shademeasurementsG=Gain which is image digitizer channel contrast O=Offsetwhich is image digitizer channel brightness x_(m) =Said normalized R_(m)(red) or G_(m) (green) or B_(m) (blue) target color values y_(m) ^(1/g)=Said normalized X_(rm) ^(1/gr) (red) or Y_(gm) ^(1/gg) (green) orZ_(bm) ^(1/gb) (blue) target tristimulus color values S=Summationvariables; (f) computing a least squares error (E) with followingformula:

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S;

(g) repeating steps (d) through (f) in order to find optimal values ofgamma (g_(r)), gain (G_(r)), and offset (O_(r)) to minimize error (E)for an X tristimulus value; (h) repeating steps (d) through (f) in orderto find optimal values of gamma (g_(g)), gain (G_(g)), and offset(O_(g)) to minimize error (E) for a Y tristimulus value; (i) repeatingsteps (d) through (f) in order to find optimal values of gamma (g_(b)),gain (G_(b)), and offset (O_(b)) to minimize error (E) for a Ztristimulus value; (j) scanning samples with an image digitizer toobtain RGB values of said samples and normalizing said RGB values ofsaid samples; (k) constructing matrix Q from following equations:##EQU14## X=Matrix of said normalized XYZ target tristimulus colorvalues

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |

Q=Matrix of said X matrices numbering total number of gray shademeasurements; (l) constructing matrices X_(rgb) and Q_(rgb) by utilizingsaid optimal values of gain (G), gamma (g), offset (O) and saidnormalized RGB values of said samples with following formulas: ##EQU15##X_(rgb) =Matrix of said X_(r) and said Y_(g) and said Z_(b) values

    Q.sub.rgb =|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN |

Q_(rgb) =Matrix of Said X_(rgb) matrices numbering total number of grayshade measurements; (m) constructing a mixing matrix M from followingequation:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1

T indicates a transposed matrix and -1 indicates an inverted matrix; (n)utilizing said mixing matrix (M) and said matrix X_(rgb) with thefollowing formula:

    X=MX.sub.rgb

to create XYZ values; and (o) storing said XYZ values on a computer forreproduction on an electronic display.
 2. A process for scanning RGBvalues of a sample utilizing an image digitizer as defined in claim 1,wherein said sample is comprised of a textile material.
 3. A process forscanning RGB values of a sample utilizing an image digitizer as definedin claim 2, wherein said textile material is comprised of carpeting. 4.A process for scanning RGB values of a sample utilizing an imagedigitizer as defined in claim 1, wherein said sample is comprised ofpaper and colorants.
 5. A process for scanning RGB values of a sampleutilizing an image digitizer and converting said RGB values of saidsample to XYZ values comprising the steps of:(a) scanning a color targetchart having gray shades with same chromaticities with an imagedigitizer to collect RGB target color values; (b) scanning said colortarget chart having gray shades with same chromaticities to collect XYZtarget tristimulus color values with a spectrophotometer; (c)normalizing said RGB target color values and said XYZ target tristimuluscolor values; (d) picking a value of gamma (g) for an X tristimuluscolor value of said target gray shades; (e) computing a least squaresfit for said picked value of gamma (g) with following formulas:##EQU16## N=Total number of gray shade measurements m=individual grayshade measurementsG=Gain which is image digitizer channel contrastO=Offset which is image digitizer channel brightness x_(m) =Saidnormalized R_(m) (red) or G_(m) (green) or B_(m) (blue) target colorvalues y_(m) ^(1/g) =Said normalized X_(rm) ^(1/gr) (red) or Y_(gm)^(1/gg) (green) or Z_(bm) ^(1/gb) (blue) target tristimulus color valuesS=Summation variables; (f) computing a least squares error (E) withfollowing formula:

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S;

(g) repeating steps (d) through (f) in order to find optimal values ofgamma (g_(r)), gain (G_(r)), and offset (O_(r)) to minimize error (E)for an X tristimulus value; (h) repeating steps (d) through (f) in orderto find optimal values of gamma (g_(g)), gain (G_(g)), and offset(O_(g)) to minimize error (E) for a Y tristimulus value; (i) repeatingsteps (d) through(f) in order to find optimal values of gamma (g_(b)),gain (G_(b)), and offset (O_(b)) to minimize error (E) for a Ztristimulus value; (j) scanning samples with an image digitizer toobtain RGB values of said samples and normalizing said RGB values ofsaid samples; (k) constructing matrix Q from following equations:##EQU17## X=Matrix of said normalized XYZ target tristimulus colorvalues

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |

Q=Matrix of said X matrices numbering the total number of gray shademeasurements; (l) constructing matrices X_(rgb) and Q_(rgb) by utilizingsaid optimal values of gain (G), gamma (g), offset (O) and saidnormalized RGB values of said samples with following formulas: ##EQU18##X_(rgb) =Matrix of said X_(r) and said Y_(g) and said Z_(b) values

    Q.sub.rgb =|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN |;

Q_(rgb) =Matrix of said X_(rgb) matrices numbering total number of grayshade measurements; (m) constructing a mixing matrix M from followingequation:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1

T indicates a transposed matrix and -1 indicates an inverted matrix; (n)utilizing said mixing matrix (M) and said matrix X_(rgb) with thefollowing formula:

    X=MX.sub.rgb

to create XYZ values; and (o) storing said XYZ values on a computer forreproduction on an electronic display.
 6. A process for scanning RGBvalues of a sample utilizing an image digitizer and converting said RGBvalues of said sample to XYZ values comprising the steps of:(a) scanninga color target chart having gray shades with same chromaticities with animage digitizer to collect RGB target color values; (b) scanning saidcolor target chart having gray shades with same chromaticities tocollect XYZ target tristimulus color values with a chroma meter; (c)normalizing said RGB target color values and said XYZ target tristimuluscolor values; (d) picking a value of gamma (g) for an X tristimuluscolor value of said target gray shades; (e) computing a least squaresfit for said picked value of gamma (g) with following formulas:##EQU19## N=Total number of gray shade measurements m=individual grayshade measurementsG=Gain which is image digitizer channel contrastO=Offset which is image digitizer channel brightness x_(m) =Saidnormalized R_(m) (red) or G_(m) (green) or B_(m) (blue) target colorvalues y_(m) ^(1/g) =Said normalized X_(rm) ^(1/gr) (red) or Y_(gm)^(1/gg) (green) or Z_(bm) ^(1/gb) (blue) target tristimulus color valuesS=Summation variables; (f) computing a least squares error (E) withfollowing formula:

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S;

(g) repeating steps (d) through (f) in order to find optimal values ofgamma (g_(r)), gain (G_(r)), and offset (O_(r)) to minimize error (E)for an X tristimulus value; (h) repeating steps (d) through (f) in orderto find optimal values of gamma (g_(g)), gain (G_(g)), and offset(O_(g)) to minimize error (E) for a Y tristimulus value; (i) repeatingsteps (d) through (f) in order to find optimal values of gamma (g_(b)),gain (G_(b)), and offset (O_(b)) to minimize error (E) for a Ztristimulus value; (j) scanning samples with an image digitizer toobtain RGB values of said samples and normalizing said RGB values ofsaid samples; (k) constructing matrix Q from following equations:##EQU20## X=Matrix of said normalized XYZ target tristimulus colorvalues

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |

Q=Matrix of said X matrices numbering total number of gray shademeasurements; (l) constructing matrices X_(rgb) and Q_(rgb) by utilizingsaid optimal values of gain (G), gamma (g), offset (O) and saidnormalized RGB values of said samples with following formulas: ##EQU21##X_(rgb) =Matrix of said X_(r) and said Y_(g) and said Z_(b) values

    Q.sub.rgb =|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN |;

Q_(rgb) =Matrix of said X_(rgb) matrices numbering total number of grayshade measurements; (m) constructing a mixing matrix M from followingequation:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1

T indicates a transposed matrix and -1 indicates an inverted matrix; (n)utilizing said mixing matrix (M) and said matrix X_(rgb) with thefollowing formula:

    X=MX.sub.rgb

to create XYZ values; and (o) storing said XYZ values on a computer forreproduction on an electronic display.
 7. A system for scanning RGBvalues of a sample utilizing an image digitizer and converting said RGBvalues of said sample to XYZ values comprising the steps of:(a) a meansfor scanning a color target chart having gray shades with samechromaticities with an image digitizer to collect RGB target colorvalues; (b) a means for scanning said color target chart having grayshades with same chromaticities to collect XYZ target tristimulus colorvalues with a colorimeter; (c) a means for normalizing said RGB targetcolor values and said XYZ target tristimulus color values; (d) a meansfor picking a value of gamma (g) for an X tristimulus color value ofsaid target gray shades; (e) a means for computing a least squares fitfor said picked value of gamma (g) with following formulas: ##EQU22##N=Total number of gray shade measurements m=individual gray shademeasurementsG=Gain which is image digitizer channel contrast O=Offsetwhich is image digitizer channel brightness x_(m) =Said normalized R_(m)(red) or G_(m) (green) or B_(m) (blue) target color values y_(m) ^(1/g)=Said normalized R_(r) ^(1/gr) (red) or Y_(gm) ^(1/gg) (green) or Z_(bm)^(1/gb) (blue) target tristimulus values S=Summation variables; (f) ameans for computing least squares error (E) with following formula:

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S;

(g) a means for repeating steps (d) through (f) in order to find optimalvalues of gamma (g_(r)), gain (G_(r)), and offset (O_(r)) to minimizeerror (E) for an X tristimulus value; (h) a means for repeating steps(d) through (f) in order to find optimal values of gamma (g_(g)), gain(G_(g)), and offset (O_(g)) to minimize error (E) for a Y tristimulusvalue; (i) a means for repeating steps (d) through (f) in order to findoptimal values of gamma (g_(b)), gain (G_(b)), and offset (O_(b)) tominimize error (E) for a Z tristimulus value; (j) a means for scanningsamples with an image digitizer to obtain RGB values of said samples andnormalizing said RGB values of said samples; (k) a means forconstructing matrix Q from the following equations: ##EQU23## X=Matrixof said normalized XYZ target tristimulus color values

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |

Q=Matrix of said X matrices numbering total number of gray shademeasurements; (l) a means for constructing matrices X_(rgb) and Q_(rgb)by utilizing said optimal values of gain (G), gamma (g), offset (O) andsaid normalized RGB values of said samples with following formulas:##EQU24## X_(rgb) =Matrix of said X_(r) and said Y_(g) and said Z_(b)values

    Q.sub.rgb -|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN|

Q_(rgb) =Matrix of said X_(rgb) matrices numbering total number of grayshade measurements; (m) a means for constructing a mixing matrix M fromfollowing equation:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1

T indicates a transposed matrix and -1 indicates an inverted matrix; (n)a means for utilizing said mixing matrix (M) and said matrix X_(rgb)with the following formula:

    X=MX.sub.rgb

to create XYZ values; and (o) a means for storing said XYZ values on acomputer for reproduction on an electronic display.
 8. A system forscanning RGB values of a sample utilizing an image digitizer as definedin claim 7, wherein said sample is comprised of a textile material.
 9. Asystem for scanning RGB values of a sample utilizing an image digitizeras defined in claim 8, wherein said textile material is comprised ofcarpeting.
 10. A system for scanning RGB values of a sample utilizing animage digitizer as defined in claim 7, wherein said sample is comprisedof paper and colorants.
 11. A system for scanning RGB values of a sampleutilizing an image digitizer and converting said RGB values of saidsample to XYZ values comprising the steps of:(a) a means for scanning acolor target chart having gray shades with same chromaticities with animage digitizer to collect RGB target color values; (b) a means forscanning said color target chart having gray shades with samechromaticities to collect XYZ target tristimulus color values with aspectrophotometer; (c) a means for normalizing said RGB target colorvalues and said XYZ target tristimulus color values; (d) a means forpicking a value of gamma (g) for an X tristimulus color value of saidtarget gray shades; (e) a means for computing a least squares fit forsaid picked value of gamma (g) with following formulas:

    D=S.sub.xx S-S.sub.x.sup.2

    G=(S.sub.xx S.sub.y -S.sub.x S.sub.xy)/D

    O=(-S.sub.x S.sub.y +S S.sub.xy)/D ##EQU25## N=Total number of gray shade measurements m=individual gray shade measurements

G=Gain which is image digitizer channel contrast O=Offset which is imagedigitizer channel brightness x_(m) =Said normalized R_(m) (red) or G_(m)(green) or B_(m) (blue) target color values Y_(m) ^(1/g) =Saidnormalized X_(rm) ^(1/gr) (red) or Y_(gm) ^(1/gg) (green) or Z_(bm)^(1/gb) (blue) target tristimulus color values S=Summation variables;(f) a means for computing a least squares error (E) with followingformula:

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S;

(g) a means for repeating steps (d) through (f) in order to find optimalvalues of gamma (g_(r)), gain (G_(r)), and offset (O_(r)) to minimizeerror (E) for an X tristimulus value; (h) a means for repeating steps(d) through (f) in order to find optimal values of gamma (g_(g)), gain(G_(g)), and offset (O_(g)) to minimize error (E) for a Y tristimulusvalue; (i) a means for repeating steps (d) through (f) in order to findoptimal values of gamma (g_(b)), gain (G_(b)), and offset (O_(b)) tominimize error (E) for a Z tristimulus value; (j) a means for scanningsamples with an image digitizer to obtain RGB values of said samples andnormalizing said RGB values of said samples; (k) a means forconstructing matrix Q from following equations: ##EQU26## X=Matrix ofsaid normalized XYZ target tristimulus color values

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |

Q=Matrix of said X matrices numbering total number of gray shademeasurements; (l) a means for constructing matrices X_(rgb) and Q_(rgb)by utilizing said optimal values of gain (G), gamma (g), offset (O) andsaid normalized RGB values of said samples with following formulas:##EQU27## X_(rgb) =Matrix of said X_(r) and said Y_(g) and said Z_(b)values

    Q.sub.rgb =|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN |;

Q_(rgb) =Matrix of said X_(rgb) matrices numbering total number of grayshade measurements; (m) a means for constructing a mixing matrix M fromfollowing equation:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1

T indicates a transposed matrix and -1 indicates an inverted matrix; (n)a means for utilizing said mixing matrix (M) and said matrix X_(rgb)with the following formula:

    X=MX.sub.rgb

to create XYZ values; and (o) a means for storing said XYZ values on acomputer for reproduction on an electronic display.
 12. A system forscanning RGB values of a sample utilizing an image digitizer andconverting said RGB values of said sample to XYZ values comprising thesteps of:(a) a means for scanning a color target chart having grayshades with same chromaticities with an image digitizer to collect RGBtarget color values; (b) a means for scanning said color target charthaving gray shades with same chromaticities to collect XYZ targettristimulus color values with a chroma meter; (c) a means fornormalizing said RGB target color values and said XYZ target tristimuluscolor values; (d) a means for picking a value of gamma (g) for an Xtristimulus color value of said target gray shades; (e) a means forcomputing a least squares fit for said picked value of gamma (g) withfollowing formulas: ##EQU28## N=Total number of gray shade measurementsm=individual gray shade measurementsG=Gain which is image digitizerchannel contrast O=Offset which is image digitizer channel brightnessx_(m) =Said normalized R_(m) (red) or G_(m) (green) or B_(m) (blue)target color values y_(m) ^(1/g) =Said normalized X_(rm) ^(1/gr) (red)or Y_(gm) ^(1/gg) (green) or Z_(bm) ^(1/gb) (blue) target tristimuluscolor values S=Summation variables; (f) a means for computing a leastsquares error (E) with following formula:

    E.sup.2 S.sub.yy =2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.x +2GOS.sub.x +G.sup.2 S;

(g) a means for repeating steps (d) through (f) in order to find optimalvalues of gamma (g_(r)), gain (G_(r)), and offset (O_(r)) to minimizeerror (E) for an X tristimulus value; (h) a means for repeating steps(d) through (f) in order to find optimal values of gamma (g_(g)), gain(G_(g)), and offset (O_(g)) to minimize error (E) for a Y tristimulusvalue; (i) a means for repeating steps (d) through (f) in order to findoptimal values of gamma (g_(b)), gain (G_(b)), and offset (O_(b)) tominimize error (E) for a Z tristimulus value; (j) a means for scanningsamples with an image digitizer to obtain RGB values of said samples andnormalizing said RGB values of said samples; (k) a means forconstructing matrix Q from following equations: ##EQU29## X=Matrix ofsaid normalized XYZ target tristimulus color values

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |

Q=Matrix of said X matrices numbering total number of gray shademeasurements; (l) a means for constructing matrices X_(rgb) and Q_(rgb)by utilizing said optimal values of gain (G), gamma (g), offset (O) andsaid normalized RGB values of said samples with following formulas:##EQU30## X_(rgb) =Matrix of said X_(r) and said Y_(g) and said Z_(b)values

    Q.sub.rgb =|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN |;

Q_(rgb) =Matrix of said X_(rgb) matrices numbering total number of grayshade measurements; (m) a means for constructing a mixing matrix M fromfollowing equation:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1

T indicates a transposed matrix and -1 indicates an inverted matrix; (n)a means for utilizing said mixing matrix (M) and said matrix X_(rgb)with the following formula:

    X=MX.sub.rgb

to create XYZ values; and (o) a means for storing said XYZ values on acomputer for reproduction on an electronic display.
 13. A process forconverting XYZ values of a sample into RGB values for electronic displaycomprising the steps of:(a) choosing a plurality of RGB color values atdifferent brightness levels; (b) measuring XYZ color values of said RGBcolor values with a color analyzer on an electronic display; (c)normalizing said RGB color values and said XYZ color values; (d) pickinga value of gamma (g) for an X tristimulus color value; (e) computing aleast squares fit for said picked value of gamma (g) with followingformulas:

    D=S.sub.xx S-S.sub.x.sup.2

    G=(S.sub.xx S.sub.y -S.sub.x S.sub.xy)/D

    O=(-S.sub.x S.sub.y S S.sub.xy)/D; ##EQU31## N=Total number of phosphor measurements m=individual phosphor measurements

G=Gain which is perceived contrast level of RGB colors O=Offset which isperceived brightness level of RGB colors x_(m) =Said normalized R_(m)(red) or G_(m) (green) or B_(m) (blue) color values y_(m) ^(1/g) =X_(rm)^(1/gr) (red) or Y_(gm) ^(1/gg) (green) or Z_(bm) ^(1/gb) (blue) forsaid normalized color values X_(rm), Y_(gm), and Z_(bm) S=Summationvariables; (f) computing a least squares error (E) with followingformula:

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S

(g) repeating steps (e) through (g) in order to find optimal values ofgamma (g_(r)), gain (G_(r)), and offset (O_(r)) to minimize error (E)for an X tristimulus value; (h) repeating steps (e) through (g) in orderto find optimal values of gamma (g_(g)), gain (G_(g)), and offset(O_(g)) to minimize error (E) for a Y tristimulus value; (i) repeatingsteps (e) through (g) in order to find optimal values of gamma (g_(b)),gain (G_(b)), and offset (O_(b)) to minimize error (E) for a Ztristimulus value; (j) constructing matrix Q from the followingequations: ##EQU32## X=Matrix of said normalized XYZ color values

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |

Q=Matrix of said X matrices numbering total number of phosphormeasurements; (k) constructing matrices X_(rgb) and Q_(rgb) by utilizingsaid optimal values of gain (G), gamma (g), offset (O) and saidnormalized RGB values of said samples with following formulas: ##EQU33##X_(rgb) =Matrix of said X_(r) and said Y_(g) and said Z_(b) values

    Q.sub.rgb =|X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN |

Q_(rgb) =Matrix of said X_(rgb) matrices numbering total number ofphosphor measurements; (l) constructing a mixing matrix M from followingequation:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1

T indicates a transposed matrix and -1 indicates an inverted matrix; (m)retrieving XYZ values of a sample from a memory of a computer in theform of a matrix X; (n) utilizing said optimal values of gain (G), gamma(g), offset (O) and mixing matrix (M) and said matrix X of said XYZvalues of a sample with the following formulas:

    X.sub.rgb =M.sup.-1 X

    R=(X.sub.r.sup.1/gr -G.sub.r)/O.sub.r

    G=(Y.sub.g.sup.1/gg -G.sub.g)/O.sub.g

    B=(X.sub.b.sup.1/gb -G.sub.b)/O.sub.b

to create RGB values of a sample; and (o) displaying said RGB values ofa sample on an electronic display.
 14. A process for converting XYZvalues of a sample into RGB values for electronic display as defined inclaim 13, wherein said sample is a textile material.
 15. A process forconverting XYZ values of a sample into RGB values for electronic displayas defined in claim 14, wherein said textile material is carpeting. 16.A process for converting XYZ values of a sample into RGB values forelectronic display as defined in claim 13, wherein said sample is paperand colorants.
 17. A process for converting XYZ values of a sample intoRGB values for electronic display as defined in claim 13, wherein saidelectronic display is a cathode ray tube.
 18. A process for convertingXYZ values of a sample into RGB values for electronic display as definedin claim 13, wherein said electronic display is a liquid crystaldisplay.
 19. A process for converting XYZ values of a sample into RGBvalues for electronic display as defined in claim 13, wherein saidelectronic display is a electroluminiscent display.
 20. A process forconverting XYZ values of a sample into RGB values for electronic displayas defined in claim 13, wherein said electronic display is a plasmadisplay.
 21. A system for converting XYZ values of a sample into RGBvalues for electronic display comprising the steps of:(a) a means forchoosing a plurality of RGB color values at different brightness levels;(b) a means for measuring XYZ color values of said RGB color values witha color analyzer on an electronic display; (c) a means for normalizingsaid RGB color values and said XYZ color values; (d) a means for pickinga value of gamma (g) for an X tristimulus color value; (e) a means forcomputing a least squares fit for said picked value of gamma (g) withfollowing formulas: ##EQU34## N=Total number of phosphor measurementsm=individual phosphor measurementsG=Gain which is perceived contrastlevel of RGB colors O=Offset which is perceived brightness level of RGBcolors x_(m) =Said normalized R_(m) (red) or G_(m) (green) or B_(m)(blue) color values Y_(m) ^(1/g) =X_(rm) ^(1/gr) (red) or Y_(gm) ^(1/gg)(green) or Z_(bm) ^(1/gb) (blue) for said normalized color valuesX_(rm), Y_(gm), and Z_(bm) S=Summation variables; (f) a means forcomputing a least squares error (E) with following formula:

    E.sup.2 =S.sub.yy -2GS.sub.y -2OS.sub.xy +O.sup.2 S.sub.xx +2GOS.sub.x +G.sup.2 S

(g) a means for repeating steps (e) through (g) in order to find optimalvalues of gamma (g_(r)), gain (G_(r)), and offset (O_(r)) to minimizeerror (E) for an X tristimulus value; (h) a means for repeating steps(e) through (g) in order to find optimal values of gamma (g_(g)), gain(G_(g)), and offset (O_(g)) to minimize error (E) for a Y tristimulusvalue; (i) a means for repeating steps (e) through (g) in order to findoptimal values of gamma (g_(b)), gain (G_(b)), and offset (O_(b)) tominimize error (E) for a Z tristimulus value; (j) a means forconstructing matrix Q from the following equations: ##EQU35## X=Matrixof said normalized XYZ color values

    Q=|X.sub.1 X.sub.2 X.sub.3 . . . X.sub.N |

Q=Matrix of said X matrices numbering the total number of phosphormeasurements; (k) a means for constructing matrices X_(rgb) and Q_(rgb)by utilizing said optimal values of gain (G), gamma (g), offset (O) andsaid normalized RGB values of said samples with the following formulas:##EQU36## X_(rgb) =Matrix of said X_(r) and said Y_(g) and said Z_(b)values

    Q.sub.rgb |X.sub.rgb1 X.sub.rgb2 X.sub.rgb3 . . . X.sub.rgbN |

Q_(rgb) =Matrix of said X_(rgb) matrices numbering total number ofphosphor measurements; (l) a means for constructing a mixing matrix Mfrom following equation:

    M=Q(Q.sub.rgb Q.sub.rgb.sup.T).sup.-1

T indicates a transposed matrix and -1 indicates an inverted matrix; (m)a means for retrieving XYZ values of a sample from a memory of acomputer in the form of a matrix X; (n) a means for utilizing saidoptimal values of gain (G), gamma (g), offset (O) and mixing matrix (M)and matrix X of said XYZ values of a sample with the following formulas:

    X.sub.rgb =M.sup.-1 X

    R=(X.sub.r.sup.1/gr -G.sub.r)/O.sub.r

    G=(Y.sub.g.sup.1/gg -G.sub.g)/O.sub.g

    B=(Z.sub.b.sup.1/gb -G.sub.b)/O.sub.b

to create RGB values of a sample; and (o) a means for displaying saidRGB values of a sample on an electronic display.
 22. A system forconverting XYZ values of a sample into RGB values for electronic displayas defined in claim 21, wherein said sample is a textile material.
 23. Asystem for converting XYZ values of a sample into RGB values forelectronic display as defined in claim 22, wherein said textile materialis carpeting.
 24. A system for converting XYZ values of a sample intoRGB values for electronic display as defined in claim 21, wherein saidsample is paper and colorants.
 25. A system for converting XYZ values ofa sample into RGB values for electronic display as defined in claim 21,wherein said electronic display is a cathode ray tube.
 26. A system forconverting XYZ values of a sample into RGB values for electronic displayas defined in claim 21, wherein said electronic display is a liquidcrystal display.
 27. A system for converting XYZ values of a sample intoRGB values for electronic display as defined in claim 21, wherein saidelectronic display is a electroluminiscent display.
 28. A system forconverting XYZ values of a sample into RGB values for electronic displayas defined in claim 7, wherein said electronic display is a plasmadisplay.
 29. A process for scanning RGB values of a sample utilizing animage digitizer as defined in claim 5, wherein said sample is comprisedof a textile material.
 30. A process for scanning RGB values of a sampleutilizing an image digitizer as defined in claim 29, wherein saidtextile material is comprised of carpeting.
 31. A process for scanningRGB values of a sample utilizing an image digitizer as defined in claim5, wherein said sample is comprised of paper and colorants.
 32. Aprocess for scanning RGB values of a sample utilizing an image digitizeras defined in claim 6, wherein said sample is comprised of a textilematerial.
 33. A process for scanning RGB values of a sample utilizing animage digitizer as defined in claim 32, wherein said textile material iscomprised of carpeting.
 34. A process for scanning RGB values of asample utilizing an image digitizer as defined in claim 6, wherein saidsample is comprised of paper and colorants.
 35. A system for scanningRGB values of a sample utilizing an image digitizer as defined in claim11, wherein said sample is comprised of a textile material.
 36. A systemfor scanning RGB values of a sample utilizing an image digitizer asdefined in claim 35, wherein said textile material is comprised ofcarpeting.
 37. A system for scanning RGB values of a sample utilizing animage digitizer as defined in claim 11, wherein said sample is comprisedof paper and colorants.
 38. A system for scanning RGB values of a sampleutilizing an image digitizer as defined in claim 12, wherein said sampleis comprised of a textile material.
 39. A system for scanning RGB valuesof a sample utilizing an image digitizer as defined in claim 38, whereinsaid textile material is comprised of carpeting.
 40. A system forscanning RGB values of a sample utilizing an image digitizer as definedin claim 12, wherein said sample is comprised of paper and colorants.